Non-commutative tori and Fourier-Mukai duality

Details Non-commutative tori and Fourier-Mukai duality Non-commutative tori and Fourier-Mukai duality

2005-09-07

arxiv.org/abs/math/0509161v1

Compos.Math.143:423-475,2007

Mathematics

Algebraic Geometry

80 pages, LaTeX2e

Scientific paper

The classical Fourier-Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to an equivalence between two dual objects. Both of these are generalized deformations of the complex tori. In one case, a complex torus is deformed formally in a non-commutative direction specified by a holomorphic Poisson structure. In the other, the dual complex torus is deformed in a B-field direction to a formal gerbe. We show these two deformations are Fourier-Mukai equivalent.

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